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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Updated: Mar 6, 2026

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A Gradient-Based Machine-Learning Inspired Inverse Modeling Approach for Characterization of Nonlinear Tissue

Hossein Geshani1, Iman Borazjani2

  • 1J. Mike Walker '66 Department of Mechanical Engineering, Texas A&M University, College Station, TX, 77840, USA.

Annals of Biomedical Engineering
|March 4, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new inverse solver to determine soft tissue properties and fiber directions from deformation data. The method efficiently recovers complex material behaviors, crucial for understanding tissue mechanics in clinical applications.

Keywords:
Gradient-based optimizationInverse problemMultilayer perceptron (MLP)Nonlinear tissue propertiesPhysics-informed machine learning

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Area of Science:

  • Biomechanics
  • Computational mechanics
  • Medical imaging analysis

Background:

  • Accurate characterization of soft tissue material properties is essential for clinical applications.
  • Understanding anisotropic nonlinear behavior and fiber directions is key for modeling tissue mechanics.

Purpose of the Study:

  • To develop and validate a gradient-based inverse solver for retrieving anisotropic nonlinear material properties and fiber directions in soft tissues.
  • To enable characterization based on known deformations and external loads, addressing a significant clinical goal.

Main Methods:

  • A gradient-based inverse solver directly minimizes nodal force residuals, avoiding repeated forward simulations.
  • Material properties are parameterized using a multilayer perceptron (MLP) mapping spatial location to behavior.
  • Residual smoothing and parallelized Jacobian computation enhance convergence speed; supports general constitutive laws.

Main Results:

  • The solver successfully recovers spatially varying elasticity and anisotropic fiber distributions in complex 3D geometries, demonstrated on a bioprosthetic heart valve.
  • A residual-only formulation offers faster optimization than Physics-Informed Neural Network (PINN) approaches.
  • While the Fung model shows parameter nonuniqueness, fiber direction recovery remains robust.

Conclusions:

  • The developed inverse solver effectively recovers nonlinear material properties and fiber directions for complex 3D soft tissue problems, including those with large deformations.
  • This method holds promise for advancing the understanding and clinical application of soft tissue mechanics.